Nonrelativistic Functional Properties in Collinear Antiferromagnets Based on Multipole Representation Theory

Abstract

In recent years, the concept of multipoles has been widely used to describe and classify various magnetic and electric responses in solids, providing a systematic way to identify symmetry-allowed or -forbidden physical responses. Conventionally, multipole classifications rely on the magnetic point group of a system, which inherently incorporates the effects of relativistic spin-orbit coupling because the spin orientation is supposed to follow the point-group transformation of the lattice. However, this approach becomes insufficient in situations where relativistic spin-orbit coupling is negligibly weak or where the spin and orbital (lattice) degrees of freedom are decoupled, thereby requiring a more comprehensive symmetry description. In this work, we introduce a multipole description on the basis of spin-point-group symmetries, enabling a systematic exploration of nonrelativistic phenomena that persist even without spin-orbit coupling in a collinear antiferromagnet. As an application, we theoretically demonstrate spin-current generation driven by elastic waves in a specific collinear antiferromagnet, fully independent of spin-orbit coupling.

Figures (2)

• Figure 1: (Color online) Lattice-rotation operation under (a) magnetic point group and (b) spin point group. In (a), the twofold rotation ($C_{2z}$) acts on both the orbital and spin degrees of freedom, whereas in (b), the operation ($[E \,\|\, C_{2z}]$) acts only on the orbital degree of freedom.
• Figure 2: (Color online) (a) (Top panel) Crystal and magnetic structures of CaMn$_2$Ge$_2$. The spin point group of the system is $\mathcal{G}_{\rm SO}^\infty \times {}^{\bar{1}} 4/ {}^{\bar{1}} m {}^1 m {}^{\bar{1}} m$ and its magnetic point group is $4'/m'm'm$. In the bottom panel, solid and dashed lines represent the inequivalent hopping strengths between the A (down spin moments) and B (up spin moments) sublattices over the distance $\sqrt{a^2 + (c/2)^2}$. (b) Band structure along the high-symmetry lines, where $\Gamma$: $\bm{0}$, ${\rm X}$: $\bm{b}_3/2$, $\Sigma$: $a^2/(2c^2)(-\bm{b}_1+\bm{b}_2+\bm{b}_3)$, ${\rm Z}$: $(\bm{b}_1+\bm{b}_2-\bm{b}_3)/2$, ${\rm N}$: $\bm{b}_2/2$, and ${\rm P}$: $(\bm{b}_1+\bm{b}_2+\bm{b}_3)/4$ with the primitive reciprocal lattice vectors $\bm{b}_1=(2\pi/a)\hat{\bm{y}}+(2\pi/c)\hat{\bm{z}}$, $\bm{b}_2=(2\pi/a)\hat{\bm{x}}+(2\pi/c)\hat{\bm{z}}$, and $\bm{b}_3=(2\pi/a)\hat{\bm{x}}+(2\pi/a)\hat{\bm{y}}$. (c) Chemical potential dependence of the spin current induced by the longitudinal elastic waves.